The non–local tail terms, if viewed from a \(D\)  dimensional calculation, arise as logarithmic corrections in the \(\varepsilon \) 
expansion. To 5PN their structure was derived by classical methods in [1]}, [2]}, see
also
[3]}, and using EFT methods in [4]}, [5]}, [6]}. Both methods lead
to the same results for the electric quadrupole moment, \(E Q_{ij} Q_{ji}\) ,[7]},
the octupole moment, \(O_{ijk} O_{ijk}\) , and the magnetic quadrupole moment, \(E J_{ij} J_{ji}\) , which develop
logarithmic and pole contributions in the
EFT–approach.
Their normalization coefficients are the same as for their imaginary part, contributing to \(dE/dt\) ,
[1]},
Eq. (4.16').For other classical calculations see [2]}. To our knowledge, there is
no other derivation yet for the failed angular momentum and memory term, but that by using EFT methods. We thank
L. Blanchet for a corresponding remark.
